Optimization of the transverse-flux motor based on design of experiments

Abstract

The objective of the paper is optimization of the outer rotor permanent-magnet transverse-flux motor using design of experiments. First, the 3-D time-stepping finite-element analysis is used to evaluate the relationship between the measured and calculated results. Further, in the 3-D time-stepping finite-element analysis a parametric model of the transverse-flux motor is coupled with an external three-phase current source to analyze the impact of the motor geometric parameters on its performance. The objectives of the motor geometry optimization are maximization of the nominal electromagnetic torque, minimization of torque pulsations, reduction of local magnetic saturation of ferromagnetic parts and increase in the current overloading regarding magnetic saturation. All the optimization objectives should be realized in a single transverse-flux motor design.

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Optimization of the Transverse-Flux Motor Based on
Design of Experiments




Janez.Leskovec@kolektor.si Bostjan.Pevec@fe.uni-lj.si Franci.Lahajnar@kolektor.si

Janez Leskovec,
Kolektor, d.d.
Slovenia
Boštjan Pevec,
University of Ljubljana
Slovenia
Franci Lahajnar,
Kolektor, d.d.
Slovenia
Damijan Miljavec
University of Ljubljana
Slovenia
miljavec@fe.uni-lj.si

Abstract—The objective of the paper is optimization of the outer
rotor permanent-magnet transverse-flux motor using design of
experiments. First, the 3-D time-stepping finite-element analysis
is used to evaluate the relationship between the measured and
calculated results. Further, in the 3-D time-stepping finite-
element analysis a parametric model of the transverse-flux
motor is coupled with an external three-phase current source to
analyze the impact of the motor geometric parameters on its
performance. The objectives of the motor geometry optimization
are maximization of the nominal electromagnetic torque,
minimization of torque pulsations, reduction of local magnetic
saturation of ferromagnetic parts and increase in the current
overloading regarding magnetic saturation. All the optimization
objectives should be realized in a single transverse-flux motor
design.

Keywords. Transverse-flux machine, finite-element method, design
of experiments
I. INTRODUCTION
The development of soft-magnetic composite materials
has increased the interest in electromagnetic structures with
the 3-D guided magnetic flux, such as the transverse-flux
motor (TFM) [1], [2]. The developed and here presented
TFM is composed of an inner stator pressed from a soft-
magnetic composite powder, outer non-magnetic rotor yoke
with permanent magnets and flux concentrators. The three-
phase coils have the form of a ring and are positioned in
stator slots. The rotor poles of each phase are shifted for 120
electrical degrees circumferentially regarding each phase.
This paper describes the use of design of experiment
(DOE) methodology to optimize the TFM performance. The
methodology, which is used for robust designing is based on
the orthogonal array recommended by Taguchi [3]. To allow
for TFM performance calculations, the finite-element analyze
(FEA) is needed. As it is much time consuming, it is more
appropriate to use the Taguchi DOE methodology instead of
evolutionary optimization algorithms. Using the TFM
geometry optimization allows for maximization of the mean
value of nominal electromagnetic torque Tmean, minimization
of torque pulsations, reduction of local magnetic saturation of
ferromagnetic parts and increase in the current overloading
regarding magnetic saturation. To achieve these optimization
goals in a single TFM design the 3-D time-stepping finite-
element analysis should be applied [4].
II. EXISTING TRANSVERSE-FLUX MOTOR

In pursuance of achieving the set of objectives we first
analyzed the already designed and tested TFM (Fig. 1). Its
outer rotor radius and the overall length were 88 mm and 100
mm, respectively. The dimensions of its stator slot was
18x6.5 mm2, the width of the stator yoke 7 mm and of the air
gap 0.5 mm, the number of pole pairs was 30 and the 16
number of turns per phase were kept constant during
optimization procedure. The values of above parameters were
determined with regard to the previous optimization of the
stator material magnetic load, electric load of coils and
induced voltage analysis. The geometry of 1/30th of the tested
TFM is presented in Fig. 2. The coils, which are inserted into
each phase stator slot, are of a circular form.


Fig. 1: Measuring set-up.

At this stage, our main concern was to evaluate the
relationship between the measured and calculated results. By
using the 3-D time-stepping FEA in which the finite-element
model was connected to an external three-phase current
source, we analyzed the TFM performance at the nominal
speed of 70 rpm. The three-phase current source presented
the switched-mode power converter with a pulse-width-
modulated voltage [5]. In the experiment phase, the prototype
was fed by imposed currents from a power converter to allow
for a comparison between the measured and calculated
results. Fig. 1 shows the measuring set-up composed of a
hysteresis break and the existing TFM. Our test results of the
measured and calculated mean electromagnetic torques are
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presented in Fig. 3. As it can be seen there is a very good
overlapping among them all over the TFM working area at
the nominal speed.
The procedure using the 3-D time-stepping FEA was
validated and approved as appropriate for further tasks used
in our optimization procedure.

Fig. 2: 3-D finite-element model of 1/30th of the built-up transverse-flux
motor.

Current amplitude [A]
Electromagnetic torque [Nm]
10
20
0
30
40
50
60
0
5
10
15
20
25
30
35
40
45
Calculated
Measured

Fig. 3: Measured and calculated results of a TFM prototype at the nominal
speed of 70 rpm


III. TFM GEOMETRY OPTIMIZATION

In the process of the TFM geometry optimization, the
main variable geometric parameters were: the axial length of
pole shoe A, ending pole-shoe width B at the air-gap side,
starting pole-shoe width C at the air-gap side and thickness of
the rotor flux concentrator D. Other TFM geometric
parameters were kept constant.
In the optimization procedure based on variable
parameters we used the Taguchi orthogonal array L9(34) [3].
Variations in the parameters, with which the DOE design area
is defined, are shown in Table I and Fig. 4.
The torques of each combination of the L9 orthogonal
array were calculated with a 3-D time-stepping finite-element
TFM model coupled with a three-phase current source. In the
experiments the current amplitude was 30A and the number
of turns per phase was 16.

IV. ELECTROMAGNETIC TORQUE MAXIMIZATION AND
TORQUE PULSATION MINIMIZATION

Results of each experiment made for the L9 orthogonal
array are shown in Table II, where Tmin is the minimal value
of the electromagnetic torque, Tmax is its maximum value and
Tmean its mean value.
As seen from Table II, there are many combinations of TFM
possible by means of which our optimization goals can be
accomplished. At this stage, our intention was to maximize
the mean value of nominal electromagnetic torque Tmean and
to minimize torque pulsations Tmax -Tmin.
A
B
C
D

Fig. 4: TFM geometry optimization parameters

TABLE I.
VARIATION OF EACH PARAMETER
Parameter Description Values
mark
2
22.5
3.5
5.5
3.5
mark
1
29.5
5
6.9
2.5
mark
3
15
2
4
4.5
Axial length of the pole shoe A [mm]
Ending pole-shoe width B [mm.]
Starting pole-shoe width C [mm]
Flux-concentrator angle D
[mech. deg.]

By implementing these TFM performance goals, the
Signal-to-Noise Ratio (SNR), as an index introduced by
Taguchi to determine the optimal combination in a series of
experiments can be calculated. In SNR, the signal represents
the mean performance and the noise the variance [3, 8]. To
enable optimization, the electromagnetic-torque mean value
will be maximized. To provide for “larger is better”, SNR can
be calculated by:
⎛
−=
∑
SNR
log10

⎟
⎠
⎟
⎞
⎜
⎝
⎜
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
n
y
i
2
1
. (1)
In minimization of the torque pulsations the opposite, i. e.
“smaller is better”, applies:

SNR
−=
log10
where yi represents the performance value.



( )
y
() n
i
∑
2
(2)
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TABLE II
RESULTS OF DOE FOR THE L9 ORTHOGONAL ARRAY
Experim. No Tmin
[Nm]
[Nm]
1 28.61 68.34
2 33.85 55.99
3 18.62 46.33
4 27.50 48.73
5 30.55 53.49
6 47.82 54.67
7 31.50 42.56
8 34.18 39.90
9 36.67 46.69

V.
LINE-VOLTAGE HIGH-HARMONICS MINIMIZATION
Tmax Tmean
[Nm]
49.37
44.93
32.52
37.11
40.05
51.45
36.17
37.50
41.80
Tmax-Tmin
[Nm]
39.73
22.14
27.71
21.23
22.94
6.85
11.06
5.72
10.02

As seen from Table II, torque pulsations (Tmax-Tmin) in the
analyzed models vary and their amplitude can be very high.
The torque mean value varies, too. The performance of TFM
strongly depends on its geometry and on the state of its
material (speaking from
electromagnetism).
Torque pulsations are composed of the time-dependent
electromagnetic torque and rotor-position-dependent cogging
torque. The latter is generally affected by the motor
geometry. Irrespective of the iron losses, the electromagnetic
torque can in case of imposed currents in the phase with
induced no-load line voltage be expressed as:
p
t
==
the perspective of

m
cuin
m
em
em
ωω
pp
−
(3)
where

( )
ω
()
c
2
b
2
a
2
c
2
cb
2
ba
2
acu,cbcu,cu,acu
3
4
sin
3
2
sinsin
RtI
RtIRtI
RiRiRipppp
⋅
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
−+
+⋅
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
−+⋅=
=⋅+⋅+⋅=++=
π
ω
π
ω
(4)
and

( )
ω
∑
=
k
∑
=
n
∑
=
k
2
⎟
⎠
⎞
⎜
⎝
⎛
−+⋅⋅ ⎟
⎠
⎞
⎜
⎝
⎛
−+
+
⎟
⎠
⎞
⎜
⎝
⎛
−+⋅⋅ ⎟
⎠
⎞
⎜
⎝
⎛
−+
+⋅+⋅⋅⋅=
=⋅+⋅+⋅=++=
n
k
n
tkUtI
tkUtI
ktkUtI
uiuiuipppp
1
ck c,
1
bk b,
1
π
aka,
ccbbaacba in
)
3
4
(sin
3
4
sin
)
3
π
2
(sin
3
π
sin
)sin(sin
ϕωω
π
ϕωω
ϕω
(5)

where tem is time-dependent electromagnetic torque, I is the
amplitude of the imposed currents, i and u are the time-
dependent currents and voltages respectively, ω is the angular
frequency, ϕ is the angle between the phase current and the
line voltage, Ua,k is the line phase a harmonic amplitude and k
are odd integers representing high harmonics.
Eqs.4 and 5 show that in most cases the shape of the time-
dependent electromagnetic torque (Eq. 3) is affected by the
presence of high-harmonic components in line voltages. High
amplitudes of high-level harmonics give evidence of the
presence of magnetic saturation in ferromagnetic parts. To
illustrate their impact on the electromagnetic torque, Fig. 5
shows calculated line voltage for the experiments N0 1, N0 6
and N0 8. The line-voltages are phase shifted between each
other, due to different power factors of experiment models.

25
00.0050.01 0.015
Time (s)
0.020.0250.03
-25
-20
-15
-10
-5
0
5
10
15
20
Voltage (V)

Ub2 Exp. 1
Ub2 Exp. 8
Ub2 Exp. 6

Fig. 5: Line voltages calculated for the experiments No 1, N0 6 and No 8.

The line-voltage shape of experiment No 1 reveals the
presence of high harmonics, whereas, the high-harmonics
line-voltage amplitudes of experiments N0 6 and No 8 are
significantly lower. Results of our analysis of the line voltage
harmonics made for each experiment are given in Table III.
Further, a comparison between results from Table II and
Table III shows an interaction between the pulsating torque
and the content of high harmonics, especially the amplitude
level of the 3rd and 5th harmonic. Consideration of the 3rd
harmonic amplitude in the optimization procedure is
appropriate for its indication of local magnetic saturation in
ferromagnetic parts of TFM. Our goal is now to define the
TFM geometry with a low amplitude of the 3rd harmonic in
the line voltage.
The mean value of the electromagnetic torque (Eqs. 3-5)
mainly depends on the line-voltage amplitude of the 1st
harmonic when TFM is supplied by an imposed current. The
high voltage level of the 1st harmonic and the low level of the
3rd one define TFM with a high level of current overloading
concerning magnetic saturation and iron losses. To take these
two facts into account in our optimization procedure, we
introduced the ratio
rdst
31
UU
made line-voltage Fourier analysis for all the nine
experiments regarding the L9 array. The results are presented
in Table III.




in order to maximize it, and
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TABLE III
HARMONIC AMPLITUDES OF THE LINE VOLTAGE FOR THE L9 ARRAY
EXPERIMENTAL MODELS
Experim.
No
1 12.51 5.30
2 10.77 4.79
3 8.42 3.55
4 10.12 4.22
5 8.76 3.62
6 11.55 3.45
7 7.98 2.35
8 9. 49 1.92
9 8.80 1.86
1st harm. 3rd harm. 5th harm. 7th harm.
2.76
2.44
2.00
1.93
1.86
1.02
0.60
0.16
0.19
1.25
1.13
0.97
0.71
0.84
0.03
0.08
0.06
0.12

VI. PERFORMANCE JOINING OPTIMISATION

Our most important optimization task was to design the TFM
geometry that would develop high mean torque with a low-
level torque pulsation, would withstand high current
overloading and would be less sensitive to the local magnetic
saturation. To assimilate the optimization goals, we defined
the so-called "performance joining" in the form given below:

()
minmax
3
1
mean
T
rd
st
TT
U
−
U
(6)
Our next step towards optimization was maximization of this
ratio (6).
Based on the results presented in Tables II and III and
paying due regard to the introduced ratios, the optimization
procedure started. The most important in the TFM
optimization procedure are Eqs. (1) and (2). Thus defined
effects of the design parameters on the set goals are presented
in Figs. 6, 7, 8, 9 and 10. For example, Fig. 6 illustrates the
SNR effect on Tmean. It is seen that the SNR combination (A2,
B3, C1 and D2) contributes to maximization of the analyzed
goal. In a similar way, minimization of the torque pulsation
and of 3rd harmonic amplitude U3
UU
and maximization of the performance joining ratio
rd, maximization of ratio
rdst
31
(6) can be obtained for any level of any factor [6, 7].
The best results for the analyzed SNR response with
respect to the studied goals are summed up in Table IV. The
values in brackets, which will be further-analyzed, show
almost the same response. The results in Figs. 6-10 show that
the most important affecting parameter is parameter A (the
axial length of the pole shoe). The reasons are the amount of
the magnetic flux entering the stator (torque capability,
saturation level) and the level of the flux leakage between the
stator teeth. The volume of the permanent magnet (parameter
D) in TFM considerably affects the level of the
electromagnetic torque production (Fig. 6) and torque
pulsations (Fig. 7), but it is of no importance for the line-
voltage 1st and 3rd harmonics.
1522.5
C
29.5
33,0
32,5
32,0
31,5
31,0
23.5
D
5
45.56.9
Fig. 6: SNR response graphs for the Tmean regarding
geometric parameters.
33,0
32,5
32,0
31,5
31,0
4.53.52.5
A
B

1522.5
C
29.5
-20
-22
-24
-26
-28
23.5
D
5
45.56.9
Fig. 7: SNR response graphs for the (Tmax-Tmin) ratio
regarding geometric parameters.
-20
-22
-24
-26
-28
4.53.5 2.5
A
B


1522.5
C
29.5
-6
-8
-10
-12
-14
23.5
D
5
45.56.9
-6
-8
-10
-12
-14
4.53.52.5
A
B

Fig. 8: SNR response graphs for U3rd regarding geometric parameters.

1522.5
C
29.5
12
10
8
23.5
D
5
45.5 6.9
12
10
8
4.53.5 2.5
A
B

Fig. 9: SNR response graphs for
rdst
31
UU
regarding geometric
parameters.
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1522.5
C
29.5
25
20
15
10
23.55
45.56.9
25
20
15
10
4.53.52.5
A
B
D

Fig. 10: SNR response graphs for Eq. (6) regarding geometric
parameters.

TABLE IV
RESULTS OF DOE FOR THE STUDIED GOALS AND GIVEN
GEOMETRIC PARAMETERS

minmax
TT
−

U

mean
T
U3rd
[V]
rd
st
3
1
U

()
minmax
3
1
mean
rd
st
TT
U
U
T
−
3
3
1
2

A
B
C
D
2
3
1
3
3
1
2
3
3
3
3
3
3
1
2(1) 3(1, 2)

As seen from Table IV, geometries (different combinations
of parameters A, B, C and D) fulfilling the optimization goals
are numerous. To get performance results for the optimized
geometries and goals (Table IV) we used the Taghouchi
prediction analyze [8]. Our findings are summarized in Table
V.
The smallest value of U3
found in model A3-B3-C3-D3 for having the lowest magnet
volume and the shortest axial length of the pole shoe.
A low level of U3
C1-D3 and A3-B3-C1-D1. The former has a low mean torque
and the latter demonstrates quite high pulsations.
As to the value of parameter D in Table IV, selected
between 3.5 or 4.5 mechanical degrees we chose the first
value since it defines a higher magnet volume and
consequently a higher TFM torque production capability.
In results given in Table V, there are two geometries of
TFM which can fulfill our goals. Values of geometric
parameters of the first geometry, named Model A
(Experiment N0 6), are: A2, B3, C1, and D2. Those of the
second one, named Model B, are: A3, B3, C1 and D2.
Electromagnetic torques calculated by using the 3-D time-
stepping finite-element TFM model coupled with a three-
phase current source are shown in Table VI.
The optimized geometry of TFM found in the model
named Model A and shown in Fig. 11 fulfills our goal of
maximizing the mean electromagnetic torque Tmean. The
geometry of TFM fulfilling the goal of the minimum
pulsating torque, high current overloading and reduced
sensitivity to local magnetic saturations is shown in Fig. 12
rd and the lowest Tmean can be
rd is also achieved with models A3-B3-
(Model B). Results of the calculated time-dependent
electromagnetic torques for both motors at 70 rpm and with
imposed three-phase currents (Iamp=30 A) are presented in
Fig. 13. The same figure shows also the calculated
electromagnetic torque at the same working point for the
existing TFM (Fig. 2).

TABLE V:
RESULTS OF THE TAGHOUCHI PREDICTION ANALYSIS OF TFM GEOMETRIES
REGARDING TABLE IV.
Model
A-B-C-D
[Nm]
[Nm]
mean
T
minmax
TT
−
U3rd
[V]
rd
st
3
1
U
U

()
minmax
3
1
mean
rd
st
T

T
U
U
T
−

Exp. N06
2-3-1-2
2-3-1-1
3-3-1-2
3-3-3-3
3-3-1-3
3-3-1-1
Existent
1-3-1-2

51.5
51.0
47.0
28.7
38.6
46.6
50.9

6.85
17.7
1.22
6.78
3.84
9.65
19.7

3.4
3.5
1.7
1.0
1.4
1.7
5.3

3.4
3.5
5.0
4.4
5.2
5.1
4.2
25.2
20.5
35.1
20.5
34.6
30.4
17.4

A comparison between the Taghouchi prediction analysis
and the 3-D time-stepping finite-element analysis is shown in
Table VII. As there is a relatively good overlapping observed
between the obtained results such prediction in similar
optimization tasks would be appropriate.

TABLE VI
TORQUES CALCULATED FOR THE OPTIMIZED AND EXISTING TFM

Tmin
[Nm]
Model A A2,B3,C1,D2 47.82
Model B A3,B3,C1,D2 42.53
Existing
TFM

Results presented in Fig. 13 show an improvement in the
mean torque capability as well as minimization of the
pulsating torque compared to the existing TFM. If is with
model B that the entire set of our goals are achieved in one
TFM geometry, i. e. maximization of Tmean, minimization of
TT
−
, minimization of
UU
and maximization of the performance joining ratio
Tmax [Nm] Tmean
[Nm]
51.45
44.63
47.80
54.67
46.14
53.14 A1,B3,C1,D2 41.09
minmax
U3
rd, maximization of
rdst
31
(6). To validate optimization achievements assured with
Model B, we did FEA at an increased amplitude of the
imposed currents (I=45A). The results are presented in Fig.
13. The mean torque values were in Models A and B
increased. Torque pulsations in Model A were increased, too.
Our conclusion is that Model A is less suitable for current
overloading than Model B speaking in terms of magnetic
saturation.
On the curves of electromagnetic torques (Fig. 13) there
are falls in their mean temporary values, due to inequality of
power factors between the three phases. The reason is that the
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